Question: Solve for $x$. $6^5=6^x\cdot6^4$ $x=$
Answer: When powers have the same base, $x^m\cdot x^n=x^{m+n}$. Let's expand the powers for ${6^5}={6^x}\cdot6^4}$. $\begin{aligned} &={\underbrace_{x\text{ times}}}\cdot\underbrace{6\cdot6\cdot6\cdot6 }_\text{4 times}} \\\\\\ &={\underbrace{6\cdot 6\cdot 6\cdot 6\cdot 6}_\text{5 times}} \\\\ \end{aligned}$ $x=1$